The optimization problem in Eq. (REF ) is to find the optimal \(\rho _{A B}\)  in \(\mathbf {S}\)  such that \(R^{\infty }\)  is minimized. \(\rho _{A B}\)  is infinite-dimensional because the attacker has the ability to arbitrarily perturb the optical mode sent by Alice into an infinite-dimensional state to send to Bob. To solve this optimization problem using numerical methods, we need to apply the photon-number cutoff assumption to \(\rho _{A B}\)  to ensure that the number of variables is in a reasonable range. A detailed description of this method can be found in Ref. [1]}.
